Robust control synthesis for uncertain linear systems with input saturation using mixed IQCs

TL;DR

This paper presents a robust control synthesis approach for uncertain linear systems with input saturation, utilizing mixed IQCs and LFR reformulation to improve stability and performance under uncertainties.

Contribution

It introduces a novel control synthesis method combining mixed IQCs with dissipation inequalities, enhancing robustness and $ ext{L}_2$-gain performance compared to traditional sector-based approaches.

Findings

Improved $ ext{L}_2$-gain performance with mixed IQCs.

Development of a scaled bounded real lemma for time-varying uncertainties.

Validation on a second-order uncertain system and cart-pendulum example.

Abstract

This paper develops a robust control synthesis method for uncertain linear systems with input saturation in the framework of integral quadratic constraints (IQCs). The system is reformulated as a linear fractional representation (LFR) that captures both dead-zone nonlinearity and time-varying uncertainties. By combining mixed IQC-based dissipation inequalities with quadratic Lyapunov functions, sufficient conditions for robust stabilization are established. Compared with conventional approaches based on a single static sector condition for the dead-zone nonlinearity, the proposed method yields improved $\mathcal{L}_2$-gain performance through the use of scaled mixed IQCs. For systems subject to time-varying structured uncertainties, a new scaled bounded real lemma is further developed based on the IQC characterization. The resulting $\mathcal{H}_\infty$ synthesis conditions are expressed as linear matrix inequalities (LMIs), which are numerically tractable in all decision variables, including the scaling factors in the IQC multipliers. The proposed method is validated using a second-order uncertain system in linear fractional form, and its superiority over an anti-windup design is further illustrated by a cart-pendulum example.